Problem: Find the greatest common factor of $210$ and $90$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $210$ and $90$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}210 &=2\cdot3\cdot5\cdot7\\\\\\\\ 90&=2\cdot3\cdot3\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}210 &=2\cdot3\cdot5\cdot7\\\\\\\\ 90&=2\cdot3\cdot3\cdot5 \end{aligned}$ Each number shares the factors ${2}, {3},$ and $5,$ so the GCF is $2\cdot3\cdot5={30}$. The greatest common factor of $210$ and $90$ is $30$.